Tuesday, March 21, 2006

Category Theory Screws You Up!

Well it does. Since I started a burst of intense category theory reading a couple of weeks ago (not that intense as I have a full time job) I've been showing unpleasant symptoms. These include insomnia, lack of concentration and grumpiness. We're not just talking correlation here, I have causal mechanisms too: how can I sleep when an example of an adjunction might pop into my mind at any moment, how can I concentrate when my brain is already fully occupied in finding those examples, and of course I'm grumpy with all this effort to understand difficult theorems that always turn out to be trivial and content-free. Fortunately I find that drugs help with the insomnia, but there's no cure for the other symptoms.

At least I haven't reached the stage where I sit down to dinner wondering whether or not my eating it is an operation with a left or right adjoint. (But I thought it didn't I, so I must be pretty far gone.) And I'm not dreaming commutative diagrams yet.

So here's my advice: if someone comes up to you in a shady bar or alleyway and offers you a monad, or an adjunction, or even an innocent little natural transformation, just say "no!".

4 Comments:

When I was an early teenager I picked up a book on CT at the local university library, after reading about 2 pages in and thinking: "Gee, if CT generalizes all these other theories, starting with it will make a great shortcut!" (like I said, a teenager ...). Anyway, when I got it home my dad, an applied mathematician, asked to see what book I had taken out. When he saw that it was CT, his reaction was probably worse than if it had been Playboy or Penthouse. My memory tells me that I first heard the classic "abstract nonsense" epithet as he then read me the riot act, but I imagine that aspect is a later reconstruction.

In retrospect, my lack of solid background on CT probably prevented me from getting better results in my dissertation ... but I am reasonably gainfully employed despite, so I guess it has worked out to my dad's satisfaction after all :) .

Right with you on this sigfpe. A few days ago I had an idea for generalising functions to arrows in a language I've been toying with for a while now - my head is just broken right now. I sleep but am not refreshed, I sit at my desk but produce nothing useful and I find myself halfway through conversations in which I have had no concious involvement.

The first time this happened to me was some fifteen years ago. I was engulfed by a game called Kye. It was a simple puzzle game, but the interesting aspect was designing your own levels. I was driving on the motorway (freeway) planning a cunning lock mechanism and found I had missed my exit by three junctions. I cannot account for that fifteen minutes of my life.

Actually, examples of category theoretical principles in casual everyday situations, if possible, would be very cool. In fact our beer debates about everything revolve around analogies all the time. I don't have good enough grasp of the TC yet, so is it naive of me to hope for a useful application of the TC even in the "field" of real life?

I studied Mathematics for 7+ years and must say that there are many hours of my life I just cannot account for. If you study abstract notions, like CT, in any science you will become engulfed. You might be able to pull yourself away for weeks, months, or even years. But, like the island on the TV show Lost it will call you back over and over again.